1. Field of the Invention
This invention relates generally to the field of methods for processing data with values at equally spaced locations in two dimensions, particularly geologic horizon data inferred from seismic information. In particular the invention concerns interpolation of data values at locations where the desired data values are missing or xe2x80x9cnullxe2x80x9d.
2. Description of the Prior Art
Prior methods for interpolation of data values at xe2x80x9cnullxe2x80x9d locations have estimated what the data value should be at a null location based on nearby valid (non-null) data which are found by scanning radially outwards from the null location in a fixed set of directions. Each of these nearby valid data values contributes an estimate or projection of what the data value should be at the null position. The final data value assigned to the null position is a weighted average of these individual projections where the weighting for each projection is designed to diminish with increasing distance of the valid data from the null position.
The prior implementation of this interpolation method has been called xe2x80x9cnull-point basedxe2x80x9d, because the method searches for a point in the two dimensional grid where interpolation is required (i.e., a null location in the grid) and performs all the steps necessary to produce the interpolated estimate at that null point location, and then moves on to search for the next null-point where interpolation is required. Prior implementations of null-point based methods have been called xe2x80x9cLinear Interpolationxe2x80x9d.
For cases involving large numbers of contiguous nulls, the prior interpolation has required a great number of calculations and increased computer time to perform them. In such cases most of the computational work is concentrated on the scanning for valid neighbors.
Identification of Objects of the Invention
A primary object of this invention is to provide an improved method for interpolation of null points in two dimensional gridded data, such as geologic horizon data inferred from seismic information, where such improved method will be referred to as Spatial Interpolation based upon radial scan interpolation methods;
An important objective of the invention is to provide an improved method where the improvement is in greatly reduced computation time, yet produces identical value interpolations as does the prior method.
Another important objective of the invention is to minimize the scanning steps required of the prior art method with an improvement in computational speed by factors of four or five or more.
The objects identified above as well as other features and advantages are incorporated in the null-line based method of the invention. According to the invention, the method, embodied in a stored computer program, searches for every linear range of contiguous nulls in various scan directions, performing for each null-line found calculations at all null points on the line in a fast recursive fashion, accumulating partial results in two intermediate arrays. After calculations for the last null-line are completed, the final interpolations are found by simple division of elements of one of the intermediate arrays by corresponding elements of the other.
The interpolations obtained by null-line based interpolation are mathematically identical to those obtained by null-point based interpolation. The difference is in the amount of work required, especially for cases involving large numbers of contiguous nulls. In such cases most of the computational work is concentrated on the scanning for valid neighbors. The null-line based approach is designed to minimize such scanning. In applications to the interpolation of gridded seismic horizon data, experience has shown computational speed improvements by factors of four or five or more, in comparing the two methods of implementation.